Mean square convergence rates for maximum quasi-likelihood estimators
نویسندگان
چکیده
منابع مشابه
Mean Square Convergence Rates for Maximum Quasi-likelihood Estimators
In this note we study the behavior of maximum quasilikelihood estimators (MQLEs) for a class of statistical models, in which only knowledge about the first two moments of the response variable is assumed. This class includes, but is not restricted to, generalized linear models with general link function. Our main results are related to guarantees on existence, strong consistency and mean square...
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I declare that this essay is my own work done as part of the Part III Examination. It is the result of my own work, and except where stated otherwise, includes nothing which was performed in collaboration. No part of this essay has been submitted for a degree or any such qualification.
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Asymptotic properties of MLEs and QMLEs of mixed regressive, spatial autoregressive models are investigated. The stochastic rates of convergence of the MLE and QMLE for such models may be less than the √ n-rate under some circumstances even though its limiting distribution is asymptotically normal. When spatially varying regressors are relevant, the MLE and QMLE of the mixed regressive, autoreg...
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Given a sequence of observations (Xn)n≥1 and a family of probability distributions {Qθ}θ∈Θ, the lossy likelihood of a particular distribution Qθ given the data Xn 1 := (X1,X2, . . . ,Xn) is defined as Qθ(B(X 1 ,D)), where B(Xn 1 ,D) is the distortion-ball of radius D around the source sequence X n 1 . Here we investigate the convergence of maximizers of the lossy likelihood.
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An order-restricted (OR) statistical model can be expressed in the general form {Pθ | θ ∈ C}, where C is a convex cone in R. In general, no unbiased estimator exists for θ. In particular, the OR maximum likelihood estimator (ORMLE) is biased, although its aggregate mean square error is usually less than that of the unrestricted MLE (URMLE). Nonetheless, the bias and mean-square error (MSE) of a...
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ژورنال
عنوان ژورنال: Stochastic Systems
سال: 2014
ISSN: 1946-5238
DOI: 10.1214/12-ssy086